Estimation of a semiparametric transformation model

Oliver Linton, Stefan Sperlich, Ingrid Van Keilegom

The Annals of Statistics · 2008 · Volume 36 · Issue 2

Abstract

This paper proposes consistent estimators for transformation parameters in semiparametric models. The problem is to find the optimal transformation into the space of models with a predetermined regression structure like additive or multiplicative separability. We give results for the estimation of the transformation when the rest of the model is estimated non- or semi-parametrically and fulfills some consistency conditions. We propose two methods for the estimation of the transformation parameter: maximizing a profile likelihood function or minimizing the mean squared distance from independence. First the problem of identification of such models is discussed. We then state asymptotic results for a general class of nonparametric estimators. Finally, we give some particular examples of nonparametric estimators of transformed separable models. The small sample performance is studied in several simulations.

Keywords

62E20, 62F12, 62G05, 62G08, 62G20, Additive models, generalized structured models, profile likelihood, semiparametric models, separability, Transformation models

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